A quadrature-based eigensolver with a Krylov subspace method for shifted linear systems for Hermitian eigenproblems in lattice QCD

TL;DR

This paper introduces a quadrature-based eigensolver combined with a Krylov subspace method for efficiently computing eigenpairs of Hermitian matrices in lattice QCD, utilizing a novel shifted CG approach to reduce computational costs.

Contribution

The paper presents a new technique for solving shifted linear systems with complex shifts in lattice QCD, improving efficiency over conventional methods.

Findings

The proposed method achieves comparable accuracy to traditional approaches.

Numerical experiments demonstrate reduced computational time.

The approach effectively handles complex shifts in Hermitian matrices.

Abstract

We consider a quadrature-based eigensolver to find eigenpairs of Hermitian matrices arising in lattice quantum chromodynamics. To reduce the computational cost for finding eigenpairs of such Hermitian matrices, we propose a new technique for solving shifted linear systems with complex shifts by means of the shifted CG method. Furthermore using integration paths along horizontal lines corresponding to the real axis of the complex plane, the number of iterations for the shifted CG method is also reduced. Some numerical experiments illustrate the accuracy and efficiency of the proposed method by comparison with a conventional method.